design of optical wdm networks using integer linear...
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Design of Optical WDM Networks using Integer Linear Programming
Network Design and Planning (2016)
Massimo Tornatore Dept. Electronics and Information
Politecnico di Milano Piazza Leonardo da Vinci 32 - 20133 Milan, Italy
WDM Network Design 2
Outline
Introduction to WDM optical networks and network design
WDM network design and optimization
– Integer Linear Programming approach
– Physical Topology Design
• Unprotected case
• Dedicated path protection case
• Shared path & link protection cases
– Notes on Traffic Grooming
– Heuristics
WDM Network Design 3
Success of optical communications Main technical reasons
Optical fiber advantages – Huge bandwidth (WDM)
– Long range transmission (EDFA optical amplifiers)
– Strength
– Use flexibility (transparency)
– Low noise
– Low cost
– Interference immunity
– ….
Optical components – Rapid technological evolution
– Increasing reliability (not for all…)
– Decreasing costs (not for all…)
Ok, but from a network perspective? – Convergence of services over a unique transport platform
WDM Network Design 4
Spectrum of the main transmission media
Lunghezza d'onda [m]
Frequenza [Hz]
Doppino
Cavo coassiale
Fibraottica
RadioAM
RadioFM
TV
10-610-510-410-310-210-1100101102103104
104 105 106 107 108 109 1010 1011 1012 1013 1014 1015
Satellite
Microonde
Lucevisibile
LF MF HF VHF UHF SHF EHF THF
LF = Low FrequencyMF = Medium FrequencyHF = High Frequency
VHF = Very High FrequencyUHF = Ultra High Frequency
SHF = Super High FrequencyEHF = Extremely High FrequencyTHF = Tremendously High Frequency
smcv
f
v
/103 8
Wavelength
Frequency
WDM Network Design 5
• Removal of water molecule absorption peak.
All-Wave Fiber… low-loss region + WDM
WDM = wavelength-
division multiplexing
(wavelength = channel)
(b) Traditional fiber (a) All-wave fiber (true wave, Leaf, etc.)
Check: http://www.thefoa.org/tech/ref/basic/SMbands.html
WDM Network Design 6
The ITU-T grid for WDM
Check: ITU-T G.694.1 Spectral grids for WDM applications: DWDM frequency grid, Feb 2012.
WDM Network Design 7
WDM optical networks: a “layered vision”
WDM layer fundamentals
– Wavelength Division Multiplexing: information is carried on high-capacity channels of different wavelengths on the same fiber
– Switching: WDM systems transparently switch optical flows in the space (fiber) and wavelength domains
WDM layer basic functions
– Optical circuit (LIGTHPATH) provisioning for the electronic layers
– Common transport platform for a multi-protocol electronic-switching environment
Optical transmission
WDM Layer
SDH ATM IP ...
... Electronic layers
Optical layers
Lightpath connection
request
Lightpath connection
provisioning
WDM Network Design 8
EO
Converter
EO
Converter
Passive Optical
Muliplexer
1300 nm
1310 nm
EO
Converter 850 nm
Ch 1
Ch 2
Ch n
What’s a WDM System?
WDM Network Design 9
EO
Converter
EO
Converter
EO
Converter
OE
Converter
OE
Converter
OE
Converter 1
2
n
Mux &
Demux
Mux &
Demux
1
2
n
WDM System Function
WDM Network Design 10
Wavelength Switching in WDM Networks
1
2
1
2
WDM Network Design 11
The concept of lightpath Example: A European WDM Network
Helsinki
Madrid
WDM Network Design 12
Outline
Introduction to WDM network design and optimization
Integer Linear Programming approach
Physical Topology Design
– Unprotected case
– Dedicated path protection case
– Shared path & link protection cases
Heuristic approach
WDM Network Design 13
WDM networks: basic concepts Logical topology
Logical topology (LT): each link represent a lightpath that could be (or has been) established to accommodate traffic
A lightpath is a “logical link” between two nodes
Full mesh Logical topology: a lightpath is established between any node pairs
LT Design (LTD): choose, minimizing a given cost function, the lightpaths to support a given traffic
Optical network access point
Electronic-layer connection request
WDM network nodes
Electronic switching node
(DXC, IP router, ATM switch, etc.)
WDM network
CR1
CR2 CR4
CR3
WDM
LOGICAL
TOPOLOGY
WDM Network Design 14
WDM networks: basic concepts Physical topology
Physical topology: set of WDM links and switching-nodes
Some or all the nodes may be equipped with wavelength converters
The capacity of each link is dimensioned in the design phase
Wavelength converter
Optical path termination
Optical Cross Connect (OXC)
WDM optical-fiber link
WDM PHYSICAL TOPOLOGY
WDM Network Design 15
Different OXC configurations
*Jane Simmons,
“Optical network design and planning”
WDM Network Design 16
1
2
Optical wavelength
channels
LP1 LP2
LP4
LP3 LP1
LP2 LP3
LP4
LP = LIGHTPATH
WDM networks: basic concepts Mapping of the logical over the physical topology
Solving the resource-allocation problem is equivalent to perform a mapping of the logical over the physical topology
– Also called Routing Fiber and Wavelength Assignment (RFWA)
Physical-network dimensioning is jointly carried out
3
Mapping is different
according to the fact
that the network is
not (a) or is (b) provided
with wavelength
converters
(a) (b)
CR1
CR2 CR4
CR3
WDM Network Design 17
Illustrative Example
WA
CA1
CA2
UT CO
TX
NE IL
MI NY
NJ PA
MD
GA UT
IL CA1
TX
WA
CO
PA
NJ
WDM Network Design 18
Static WDM network planning Problem definition
Input parameters, given a priori
– Physical topology (OXC nodes and WDM links)
– Traffic requirement (logical topology)
• Connections can be mono or bidirectional
• Each connection corresponds to one lightpath than must be setup between
the nodes
• Each connection requires the full capacity of a wavelength channel (no traffic
grooming)
Parameters which can be specified or can be part of the problem
– Network resources: two cases
• Fiber-constrained: the number of fibers per link is a preassigned global
parameter (typically, in mono-fiber networks), while the number of
wavelengths per fiber required to setup all the lightpaths is an output
• Wavelength-constrained: the number of wavelengths per fiber is a
preassigned global parameter (typically, in multi-fiber networks) and the
number of fibers per link required to setup all the lightpaths is an output
WDM Network Design 19
Static WDM network planning Problem definition (II)
Physical constraints
– Wavelength conversion capability
• Absent (wavelength path, WP or transparent)
• Full (virtual wavelength path, VWP or opaque)
• Partial (partial virtual wavelength path, PVWP)
– Propagation impairments
• The length of lightpaths is limited by propagation phenomena (physical-
length constraint)
• The number of hops of lightpaths is limited by signal degradation due to the
switching nodes
– Connectivity constraints
• Node connectivity is constrained; nodes may be blocking
Links and/or nodes can be associated to weights
– Typically, link physical length is considered
WDM Network Design 20
Routing can be
– Constrained: only some possible paths between source and destination
(e.g. the K shortest paths) are admissible
• Great problem simplification
– Unconstrained: all the possible paths are admissible
• Higher efficiency in network-resource utilization
Cost function to be optimized (optimization objectives)
– Route all the lightpaths using the minimum number of wavelengths
(physical-topology optimization)
– Route all the lightpaths using the minimum number of fibers (physical-
topology optimization)
– Route all the lightpaths minimizing the total network cost, taking into
account also switching systems (physical-topology optimization)
Static WDM network optimization Problem definition (III)
WDM Network Design 21
Routing and Wavelength Assignment (RWA) [OzBe03]
– The capacity of each link is given
– It has been proven to be a NP-complete problem [ChGaKa92]
– Two possible approaches
• Maximal capacity given maximize routed traffic (throughput)
• Offered traffic given minimize wavelength requirement
Routing Fiber and Wavelength Assignment (RFWA)
– The capacity of each link is a problem variable
– Further term of complexity Capacitated network
– The problem contains multicommodity flow (routing), graph coloring
(wavelength) and localization (fiber) problems
– It has been proven to be a NP-hard problem (contains RWA)
Static WDM network optimization Complexity
WDM Network Design 22
Optimization problems Classification
Optimization problem – optimization version
– Find the minimum-cost solution
Optimization problem – decision version (answer is yes or no)
– Given a specific bound k, tell me if a solution x exists such that x<k
Polynomial problem
– The problem in its optimization version is solvable in a polynomial time
NP problem
– Class of decision problems that, under reasonable encoding schemes, can be solved by polynomial time non-deterministic algorithms
NP-complete problem
– A NP problem such that any other NP problem can be transformed into it in a polynomial time
– The problem is very likely not to be in P
– In practice, the optimization-problem solution complexity is exponential
NP-hard problem
– The problem in its decision version is not solvable in a polynomial time (is NP-complete) the optimization problem is harder than an NP-problem
– Contains an NP-complete problem as a subroutine
WDM Network Design 23
Dimensions of Complexity…
Routing
Wavelength
Fiber Time
Physical
layer
Applications
Mixed Rates
Protection
Grooming
Energy
Vendors Domains
Cost
WDM Network Design 24
WDM network optimal design is a very complex problem. Various
approaches proposed
– Mathematical programming (MP)
• Exact method (guarantees optimal solution)
• Computationally expensive, not scalable
– Heuristic methods
• An alternative to MP for realistic dimension problems
According to the cost function, the problem is
– Linear
– Non linear
Optimization problem solution Optimization methods
WDM Network Design 25
Outline
Introduction to WDM network design and optimization
Integer Linear Programming approach
Physical Topology Design
– Unprotected case
– Dedicated path protection case
– Shared path & link protection cases
Heuristic approach
WDM Network Design 26
WDM-network static-design problem can be solved with the mathematical
programming techniques
– In most cases the cost function is linear linear programming
– Variables can assume integer values integer linear programming
LP solution
– Variables defined in the real domain
– The well-known computationally-efficient Simplex algorithm is employed
ILP solution
– Variables defined in the integer domain
– The optimal integer solution is found by exploring all integer admissible solutions
• Branch and bound technique: admissible integer solutions are explored in a tree-like
search
Optimization problem solution Mathematical programming solving
WDM Network Design 27
A arduous challenge
– NP-completeness/hardness coupled with a huge number of variables
• In many cases the problem has a very high number of solutions (different
virtual-topology mappings leading to the same cost-function value)
– Practically tractable for small networks
Simplifications
– RFWA problem decomposition: e.g., first routing and then f/w assignment
– Constrained routing (route formulation, see in the following)
– Relaxed solutions (randomized rounding)
– Other methodologies:
• Column generation, Lagrangean relaxation, etc..
ILP, when solved with approximate methods, loses one of its main
features: the possibility of finding a guaranteed minimum solution
– Still ILP can provide valuable solutions
ILP application to WDM network design Approximate methods
WDM Network Design 28
Simplification can be achieved by removing the integer constraint
– Connections are treated as fluid flows (multicommodity flow problem)
• Can be interpreted as the limit case when the number of channels and
connection requests increases indefinitely, while their granularity becomes
indefinitely small
• Fractional flows have no physical meaning in WDM networks as they would
imply bifurcation of lightpaths on many paths
– LP solution is found
In some cases the closest upper integer to the LP cost function can
be taken as a lower bound to the optimal solution
Not always it works…
See [BaMu96]
ILP application to WDM network design ILP relaxation
WDM Network Design 29
l,k: link identifiers (source and destination nodes)
Fl,k: number of fibers on the link l,k
l,k: number of wavelengths on the link l,k
cl,k: weight of link l,k (es. length, administrative weight, etc.)
– Usually equal to ck,l
The ILP models: Notation
l
k
WDM Network Design 30
Cost functions Some examples
RFWA
– Minimum fiber number M
• Terminal equipment cost
– VWP case
– Minimum fiber mileage (cost) MC
• Line equipment [BaMu00]
RWA
– Minimum wavelength number
– Minimum wavelength mileage
• [StBa99],[FuCeTaMaJa03]
– Minimum maximal wavelength number on a link
• [Mu97]
MFkl
kl minmin),(
,
C
kl
klkl MFc minmin),(
,,
minmin),(
,
kl
kl
C
kl
klklc minmin),(
,,
MAXklkl
min]max[min ,,
WDM Network Design 31
Outline
Introduction to WDM network design and optimization
Integer Linear Programming approach
Physical Topology Design
– Unprotected case
– Dedicated path protection case
– Shared path & link protection cases
References
WDM Network Design 32
Approaches to WDM design
Two basilar and well-known approaches [WaDe96],[Wi99]
– FLOW FORMULATION (FF)
– ROUTE FORMULATION (RF)
WDM Network Design 33
Flow Formulation (FF)
Flow variable
Flow on link (l,k) due to a request generated by to source-destination couple
(s,d)
Fixed number of variables
Unconstrained routing
ds
klx ,
,
s d
1 2
3 4
ds
s
ds
s
x
x,
1,
,
,1
ds
s
ds
s
x
x,
,3
,
3,
dsds xx ,
1,2
,
2,1
dsds xx ,
3,4
,
4,3 ds
d
ds
d
x
x,
,4
,
4,
ds
d
ds
d
x
x,
2,
,
,2
ds
ds
x
x,
1,3
,
3,1 ds
ds
x
x,
2,4
,
4,2
WDM Network Design 34
Variables represent the amount of traffic (flow) of a given traffic
relation (source-destination pair) that occupies a given channel (link,
wavelength)
Lightpath-related constraints
– Flow conservation at each node for each lightpath (solenoidal constraint)
– Capacity constraint for each link
– (Wavelength continuity constraint)
– Integrity constraint for all the flow variables (lightpath granularity)
Allows to solve the RFWA problems with unconstrained routing
A very large number of variables and constraint equations
ILP application to WDM network design Flow Formulation (FF)
WDM Network Design 35
ILP application to WDM network design Flow formulation fundamental constraints
Solenoidality constraint
– Guarantees spatial continuity of the
lightpaths (flow conservation)
– For each connection request, the
neat flow (tot. input flow – tot. output
flow) must be:
• zero in transit nodes
• the total offered traffic (with
appropriate sign) in s and d
Capacity constraint
– On each link, the total flow must not
exceed available resources
(# fibers x # wavelengths)
Wavelength continuity constraint
– Required for nodes without
converters
1
2
3
4
5
6
s d
WDM Network Design 36
Notation
c: node pair (source sc and destination dc) having requested one or
more connections
xl,k,c: number of WDM channels carried by link (l,k) assigned to a
connection requested by the pair c
Al: set of all the nodes adjacent to node i
vc: number of connection requests having sc as source node and dc
as destination node
W: number of wavelengths per fiber
λ: wavelength index (λ={1, 2 … W})
WDM Network Design 37
Unprotected case VWP, FF
(l,k)F
c,(l,k)x
klFWx
clslv
dlv
xx
kl
ckl
c
klckl
Ak Ak
cc
cc
cklclk
l l
integer
integer Integrity
),(Capacity
,
otherwise0
if
if
itySolenoidal
,
,,
,,,
,,,,
N.B. from now on, notation “l,k” implies l k
WDM Network Design 38
Note, the unsplittable case!
(l,k)F
c,(l,k)x
klFWxv
clsl
dl
xx
kl
ckl
c
klcklc
Ak Ak
c
c
cklclk
l l
integer
binary Integrity
),(Capacity
,
otherwise0
if1
if1
itySolenoidal
,
,,
,,,
,,,,
WDM Network Design 39
Homework
What happens in the bidirectional case?
– i.e., Each transmission channel provides the same capacity λ in both
directions.
WDM Network Design 40
Extension to WP case
In absence of wavelength converters, each lightpath has to preserve
its wavelength along its path
This constraint is referred to as wavelength continuity constraint
In order to enforce it, let us introduce a new index in the flow
variable to analyze each wavelength plane
The structure of the formulation does not change. The problem is
simply split on different planes (one for each wavelength)
The vc traffic is split on distinct wavelengths vc,λ
The same approach will be applied for no-flow based formulations
,,,,, cklckl xx
WDM Network Design 41
Unprotected case WP, FF
,integer
integer
,integer
Integrity
),,(Capacity
,,
otherwise0
if
if
itySolenoidal
,
,
,,,
,,,,
,
,
,
,,,,,,
cv
(l,k)F
c,(l,k)x
klFx
cvv
clslv
dlv
xx
c
kl
ckl
c
klckl
cc
Ak Ak
cc
cc
cklclk
l l
WDM Network Design 42
Flow (FF) vs Route (RF) Formulation
Variable xl,s,d: flow on link i
associated to source-destination
couple s-d
Variable rp,s,d: number of
connections s,d routed on the
admissible path p
r1,s,d
r2,s,d
r3,s,d
Fixed number of variables
Unconstrained routing
Constrained routing
-k-shortest path
Sub-optimality?
FLOW ROUTE
s d s d
1 2
3 4
ds
s
ds
s
x
x,
1,
,
,1
ds
s
ds
s
x
x,
,3
,
3,
dsds xx ,
1,2
,
2,1
dsds xx ,
3,4
,
4,3 ds
d
ds
d
x
x,
,4
,
4,
ds
d
ds
d
x
x,
2,
,
,2
ds
ds
x
x,
1,3
,
3,1 ds
ds
x
x,
2,4
,
4,2
WDM Network Design 43
All the possible paths between each sd-pair are evaluated a priori
Variables represent which path is used for a given connection
– rpsd: path p is used by rpsd connections between s and d
Path-related constraints
– Routing can be easily constrained (e.g. using the K-shortest paths)
• Yen’s algorithm
– Useful to represent path-interference
• Physical topology represented in terms of interference (crossing) between
paths (e.g. ipr = 1 (0) if path p has a link in common with path r)
Number of variables and constraints
– Very large in the unconstrained case,
– Simpler than flow formulation when routing is constrained
WDM mesh network design Route formulation
WDM Network Design 44
Unprotected case VWP, RF
(l,k)F
n)cr
klFWr
cvr
kl
nc
Rrklnc
n
cnc
klnc
integer
,( integer Integrity
),(Capacity
itySolenoidal
,
,
,,
,
,,
New symbols
– rc,n: number of connections routed on the n-th admissible path between source
destination nodes of the node-couple c
– R(l,k): set of all admissible paths passing through link (l,k)
WDM Network Design 45
Unprotected case WP, RF
,integer
integer
,,( integer
Integrity
),,(Capacity
,
itySolenoidal
,
,
,,
,,,
,
,,,
,,
cv
(l,k)F
n)cr
klFr
cvv
cvr
c
kl
nc
Rr
klnc
cc
n
cnc
klnc
Analogous extension to FF case
– rc,n,λ = number of connection routed on the n-th admissible path between node pair
c (source-destination) on wavelength λ
WDM Network Design 46
ILP source formulation New formulation derived from flow formulation
Reduced number of variables and constraints
compared to the flow formulation
Allows to evaluate the absolute optimal
solution without any approximation and with
unconstrained routing
Can not be employed in case path protection
is adopted as WDM protection technique
– Does not support link-disjoint routing
WDM Network Design 47
ILP source formulation Source Formulation (SF) fundamental constraints
New flow variable
– Flow carried by link l and having node s as source
– Flow variables do not depend on destinations anymore
Solenodality – Source node
• the sum of xl,k,s variables is equal to the total number of requests originating in the node
– Transit node
• the incoming traffic has to be equal to the outgoing traffic plus the nr. of lightpaths terminated in the node
d
ds
klskl xx ,
,,,
WDM Network Design 48
ILP source formulation An example
2 connections requests
– 1 to 4
– 1 to 3
Solution
– X1,2,1,X1,6,1, X2,3,1, X6,5,1,X,5,3,1,X,3,41= 1
– Otherwise X,l,k,1= 0
1° admissible solution
– LA 1-2-3-4
– LB 1-6-5-3
2° admissible solution
– LA 1-2-3
– LB 1-6-5-3-4
Both routing solutions are
compatible with the same SF solution
1
2 3
4
5 6
3
WDM Network Design 49
Unprotected case VWP, SF
(l,k)F
i,(l,k)x
klFWx
liliCxx
iSCx
kl
ikl
i
klikl
Ak Ak
liiklilk
Ak j
ijiiki
l l
i
integer
integer Integrity
),(Capacity
)(,itySolenoidal
,
,,
,,,
,,,,,
,,,
New symbols
– xl,k,i : number of WDM channels carried by link l, k assigned connections originating
at node i
– Ci, j: number of connection requests from node i to node j
See [ToMaPa02]
WDM Network Design 50
Unprotected case WP, SF
)(,,,integer
,integer
integer
,,integer
Integrity
),,(Capacity
)(,,
)(,,,
,
itySolenoidal
,,
,
,
,,,
,,,,
,,,
,,,,,,,,
,,
,,,,
lijic
is
l,kF
il,kx
klFx
liliCc
lilicxx
iCSs
isx
li
i
kl
ikl
i
klikl
lili
Ak Ak
jiiklilk
l
liii
Ak
iiki
l l
i
Analogous extension to FF case
WDM Network Design 51
ILP source formulation Two-step solution of the optimization problem
The source formulation variables xl,k,s and Fl,k
– Do not give a detailed description of RWFA of each single lightpath
– Describe each tree connecting a source to all the connected
destination nodes (a subset of the other nodes)
– Define the optimal capacity assignment (dimensioning of each link in
terms of fibers per link) to support the given traffic matrix
STEP 1: Optimal dimensioning computation by exploiting SF
(identification problem, high computational complexity)
STEP 2: RFWA computation after having assigned the number of
fibers of each link evaluated in step 1 (multicommodity flow problem,
negligible computational complexity)
WDM Network Design 52
ILP source formulation Complexity comparison between SF and FF
The second step has a negligible impact on the SF computational time
– Fl,k are no longer variables but known terms
Fully-connected virtual topology: C = N (N-1), S=N
– Worst case (assuming L << N (N-1))
LWCWRCWL)C(W
L L) C(W C N C) L W(
LCSLSWSCNSLW
LRCCL
CLNCL
SLNSL
221route WP
2212flow WP
2)2()2(source WP
22route VWP
)1(22flow VWP
)1(22source VWP
variab.#const. #nFormulatio
NN
NN
OO WP
OOVWP
variab.# FF/SFconst. # FF/SFCase
Fully connected virtual topology
– Symbols
• N nodes
• L links
• R average number of paths per node pair
• W wavelengths per fiber
• C connection node-pairs
• S source nodes requiring connectivity
WDM Network Design 53
Case-study networks Network topology and parameters
N = 14 nodes
L = 22 (bidir)links
C = 108 connected pairs
360 (unidir)conn. requests
NSFNET EON
Palo Alto CA
San Diego CA
Salt Lake City UT
Boulder CO
Houston TX
Lincoln
Champaign
Pittsburgh
Atlanta
Ann Arbor
Ithaca
Princeton
College Pk.
Seattle WA
N = 19 nodes
L = 39 (bidir)links
C = 342 connected pairs
1380 (unidir)conn. requests
Static traffic matrices derived from real traffic measurements
Hardware: 1 GHz processor, 460 Mbyte RAM
Software: CPLEX 6.5
WDM Network Design 54
Case-study networks SF vs. FF: variables and constraints (VWP)
The number of constraints decreases by a factor
– 9 for the NSFNet
– 26 for the EON
The number of variables decreases by a factor
– 8.5 for the NSFNet
– 34 for the EON
These simplifications affect computation time and memory occupation, achieving relevant savings of computational resources
Rete/Form vincoli variabili
NsfNet/source 284 570
NsfNet/flow 2552 4840
EON/source 517 1560
EON/flow 13650 53430
Network/Formulation # const. # variab.
WDM Network Design 55
Case-study networks SF vs. FF: variables and constraints (WP)
In the WP case
– The number of variables and constraints linearly increases with W
– The gaps in the number of variables and constraints between FF and
SF increase with W
The advantage of source formulation is even more relevant in the
WP case
0
1 1 0 5
2 1 0 5
3 1 0 5
4 1 0 5
5 1 0 5
0 2 4 6 8 1 0 1 2 1 4 1 6
E O N W P
s o u r c e v a r i a b l e s f l o w v a r i a b l e s s o u r c e c o n s t r a i n t s f l o w c o n s t r a i n t s
Number of wavelengths, W
Num
be
r o
f va
ria
ble
s a
nd
co
nstr
ain
ts
WDM Network Design 56
Case-study networks SF vs. FF: time, memory and convergence
The values of the cost function Msource obtained by SF are always equal or better (lower) than the corresponding FF results (Mflow)
Coincident values are obtained if both the formulations converge to the optimal solution
– Validation of SF by induction
Memory exhaustion (Out-Of-Memory, O.O.M) prevents the convergence to the optimal solution. This event happens more frequently with FF than with SF
W SF FF
2 27m 40m
4 28m 105m
8 36s 50m
16 6m 10h
32 19m 5h
Computational time Memory occupation
W SF FF
2 0.39MB 1.3MB
4 O.O.M O.O.M
8 5MB 42MB
16 47MB O.O.M
32 180MB O.O.M
WDM Network Design 57
Outline
Introduction to WDM network design and optimization
Integer Linear Programming approach
Physical Topology Design
– Unprotected case
– Dedicated path protection case
– Shared path & link protection cases
Heuristic approach
WDM Network Design 58
Protection in WDM Networks (1) Motivations (bit rate)
Today WDM transmission systems allow the multiplexing on a single
fiber of up to 160 distinct optical channels
– recent experimental systems support up to 256 channels:
A single WDM channel carries from 2.5 to 40 Gb/s (ITU-T G.709)
The loss of a high-speed connection operating at such bit rates,
even for few seconds, means huge waste of data !!
The increase in WDM capacity associated with the tremendous
bandwidth carried by each fiber and the evolution from ring to mesh
architectures brought the need for suitable protection strategies into
foreground.
Example: 1ms outage for a 100G x 100Waves fiber [10Tbit/s] means
10Gbit=1.25Gbyte of data lost (n.b.: 1 cd-rom is 0.9 GByte)
WDM Network Design 59
Protection in WDM Networks (2) Motivations (network dimension)
Even though fiber are very resilient, the geographical dimension of a
backbone network lead to very high chances that the network is
operating in a fault state.
Example: failure per 1000Km per year (2001 statistics) ≈ 2 (*)
What happens on a continental network?! Hundreds of failures….
1
3
2
610
45
78
9
12
13
14
11
1200
2100
4800
3000
1500
3600
1200
2400
3900
1200
2100
3600
1500
2700
1500
1500
600
600
1200
1500
600
300
(*) Source www.southern-telecom.com/AFL%20Reliability.pdf
WDM Network Design 60
Immediate Causes of Fiber Cable Failures
Dig-ups
58.10%
Other
9.70%
Fallen Trees
1.30%
Excavation
1.30%Flood
1.30%
Firearm
1.30%
Vehicle
7.50%
Process Error
6.90%
Power Line
4.40%
Sabotage
2.50%
Rodent
3.80%
Fire
1.90%
Source: D. E. Crawford, “Fiber Optic Cable Dig-ups – Causes and Cures,” A Report to The Nation
– Compendium of Technical Papers, pp. 1-78, FCC NRC, June 1993
WDM Network Design 61
Customer’s concerns: Bandwidth Availability
Fee etc.
Operator’s concerns: Resource Protection Penalty
Network design decisions for protection are very important
SLA and Provisioning
WDM Network Design 62
3 performance metrics for protection
Resource occupation (resource overbuild)
Availability – Probability to find the service up
Protection Switching Time
Availability goes in tradeoff with the other two!!
WDM Network Design 63
Dedicated Path Protection (DPP)
1+1 or 1:1 dedicated protection (>50% capacity for protection)
– Both solutions are possible
– Each connection-request is satisfied by setting-up a lightpath pair of a working + a protection lightpaths
– RFWA must be performed in such a way that working and protection lightpaths are link disjoint
Additional constraints must be considered in network planning and optimization
Transit OXCs must not be reconfigured in case of failure
The source model can not be applied to this scenario
WDM Network Design 64
“Max half” formulation (MH) Equation set (VWP case)
This formulation does not need an upgrade of unprotected flow variable
See [ToMaPa04]
(l,k)F
(l,k)cx
klFWx
clvxx
cidiv
div
xx
kl
ckl
c
klckl
cclkckl
kl kl
cc
cc
cklckl
i i
integer
, integer Integrity
),(Capacity
, HalfMax
),(
otherwise 0
if2
if2
itySolenoidal
,
,,
,,,
,,,,
),( ),(
,,,,
I I
WDM Network Design 65
“Max half” formulation (MH) Limitations
Same number of variables and constraints as the unprotected
flow formulation
Allows to evaluate the absolute optimal solution without any
approximation and with unconstrained routing in almost all cases
Requires an a posteriori control to verify the feasibility of obtained
solution
Problem:
In conclusion, each
unity of flow
must be modelled
independently, such that
it can be protected
independently
WDM Network Design 66
Dedicated Path Protection (DPP) Flow formulation, VWP
(l,k)F
(l,k)c,tx
klFWx
tcklxx
tclsl
dl
xx
kl
tckl
tc
kltckl
tclktckl
Ak Ak
c
c
tckltclk
l l
integer
),( binary Integrity
,Capacity
,,, 1disjoint-Link
,,
otherwise 0
if2
if2
itySolenoidal
,
,,,
),(
,,,,
,,,,,,
,,,,,,
New symbols
– xl,k,c,t = number of WDM channels carried by link (l,k) assigned to the t-th
connection between source-destination couple c
Rationale: for each connection request, route a link-disjoint connection
route two connections and enforce link-disjointness between them.
WDM Network Design 67
Dedicated Path Protection (DPP) Route formulation (RF), VWP
l,kF
ntcr
klFWr
kltcr
tcr
kl
ntc
Rr
klntc
RRr
ntc
n
ntc
klntc
lkklntc
integer
,, binary Integrity
,Capacity
,,, 1disjoint-Link
, 2itySolenoidal
,
,,
,,,
,,
,,
,,,
,,,,
New symbols
– rc,n,t = 1 if the t-th connection between source destination node couple c is routed on the n-th admissible path
– R(l,k) = set of all admissible paths passing through link (l,k)
WDM Network Design 68
Dedicated Path Protection (DPP) Route formulation (RF) II, VWP
l,kF
ncr
klFWr
cvr
kl
nc
Rr
klnc
n
cnc
klnc
integer
,integer 'Integrity
,'Capacity
'itySolenoidal
,
,
''
,,
,
,,
Substitute the single path variable rc,n by a protected route variable r’c,n (~ a cycle)
No need to explicitly enforce link disjointness
Identical formulation to unprotected case
How do we calculate the minimum-cost disjoint paths? Suurballe
WDM Network Design 69
Dedicated Path Protection (DPP) Flow formulation, WP
c,v
l,kF
l,kc,tx
klFx
tcklxx
cv
tclslvdlv
xx
tc
kl
tckl
tc
kltckl
tclktckl
tc
Ak Ak
ctc
ctc
tckltclk
l l
bynary
integer
,, binary
Integrity
,,Capacity
,,, 1disjoint-Link
2
;,,, otherwise 0
if if
itySolenoidal
,,
,
,,,,
),(
,,,,,
,,,,,,,,,
,,
,,
,,
,,,,,,,,
New symbols
– xl,k,c,t ,λ= number of WDM channels carried by wavelength λ on link l,k
assigned to the t-th connection between source-destination couple c
– Vc,λ= traffic of connection c along wavelength λ
WDM Network Design 70
Dedicated Path Protection (DPP) Route formulation (RF), WP
),(bynary
integer
,),,( binary
Integrity
),,(Capacity
),(),,( 1disjoint-Link
, 2
),,(
itySolenoidal
,,
,
,,,
,,,,
,,,
,,
,,,,,
,,,,
,,,,,
c,tv
l,kF
ntcr
klFr
kltcr
tcv
tcvr
tc
kl
ntc
Rr
klntc
RRr
ntc
tc
n
tcntc
klntc
lkklntc
WDM Network Design 71
Dedicated Path Protection (DPP) Route formulation (RF) II, WP
l,kF
ncr
klFrr
cvv
cvr
kl
nc
Rr
kl
Rr
ncnc
cc
ncnc
klnc klnc
integer
,,integer 'Int.
,,''Cap.
, '
Solen.
,
2,1,,,
1
''
,
''
,,,,
,
,
2,1,,,
21
2 ,2,1,, 2 ,1,2,,
1,22,1
21
2,1
2,12,1
rc,n,λ = number of connections between source-destination couple c routed on the n-th admissible couple of disjoint paths having one path over wavelength λ1and the other over λ2
WDM Network Design 72
Complexity comparison between DPP RF-WP formulations
Nr of variables for rctnλ -> R x C x T x W
– R x C number of single route variables
Nr of variables for rcnλ’λ’’ -> R’ x C x W2
– R’ x C number of protected route variables
– For R=R’, this is preferable if T>W
WDM Network Design 73
Outline
Introduction to WDM network design and optimization
Integer Linear Programming approach
Physical Topology Design
– Unprotected case
– Dedicated path protection case
– Shared path & link protection cases
References
WDM Network Design 74
Shared Path Protection (SPP)
Protection-resources sharing
– Protection lightpaths of different
channels share some wavelength
channels
– Based on the assumption of single point of failure
– Working lightpaths must be link (node) disjoint
Very complex control issues
– Also transit OXCs must be reconfigured in case of failure
• Signaling involves also transit OXCs
• Lightpath identification and tracing becomes fundamental
Sharing is a way to decrease the
capacity redundancy and the number
of lightpaths that must be managed
WDM Network Design 75
How to model SPP: the Link Vector (1)
Given: – Graph G(V,E)
– Set of connections Li
(already routed)
Link vector
Specified in IETF (see, e.g., RSVP-TE Extensions For Shared-Mesh Restoration in Transport Networks )
e'
e'
*
e
e'
e
e'
ee
max
)}(e'0 E, e' |{
e
WDM Network Design 76
e1
e2
e3
e4
e5
e6
e7 e8
A B
C
e2 e3 e4 e5 e6 e7 *
5ee1 e8
Connection A arrival: e5 ( 0, 1, 1, 0, 0, 0, 0, 0 ) 1
( 1, 2, 1, 0, 0, 0, 0, 0 ) 2
Initial state :e5
How to model SPP: the Link Vector (2)
(a) Sample network and connections
(a) Evolution of link vector for e5
( 0, 0, 0, 0, 0, 0, 0, 0 ) 0
( 1, 2, 1, 0, 0, 0, 1, 0 ) 2
Connection B arrival: e5
Connection C arrival: e5
WDM Network Design 77
Flow Formulation
– Binary variables xl,k,c,t,p associated to
the flow on each link l,k for each
single connection request c,t (p=w
working flow, p=s protection flow)
Route Formulation
– 1° approach: integer variables rc,n
associated to each simple path n
joining the node pair c (e.g. s,d).
– 2° approach: integer variables r’c,n
associated to the n-th possible
working-spare route pair that joins
each s-d node pair c
Two ILP approaches for SPP
r1,s,d s d
r2,s,d
r3,s,d
s d
xs,a,c,1,w xa,d,c,1,w
Connection request c,1
Explore Shared path protection by both classical approaches
xs,a,c,1,p xa,d,c,1,p
Xs,b,c,1,w
xs,b,c,1,p Xb,d,c,1,w
xb,d,c,1,p
a
b
WDM Network Design 78
How to calculate «max» in ILP
(l,k) F
c,(l,k) xIntegrity
(l,k)FWxCapacity
(l,k)xT
l,c
otherwise
sif lv
dif lv
xxitySolenoidal
xObjective
l,k
l,k,c
c
l,kl,k,c
l,k,c
Ak Ak
cc
cc
l,k,ck,l,c
l,k,c
l l
integer
integer
max
0
Tmin ) (max min
c
c
k)(l,
WDM Network Design 79
Shared Path Protection (DPP) Flow formulation, VWP
),(,),( binary
integer
),( binary
Integrity
),(,),( ,
1Sharing
),(,
,
Capacity
,,, 1disjoint-Link
;,,
otherwise 0
if1
if1
;,,
otherwise 0
if1
if1
itySolenoidal
,
,
,,,
,,,,,,,,
,,,,,,,
),(
,
),(
,,,,
,,,,,,,,,,,,
,,,,,,
,,,,,,
ji(l,k)c,tz
(l,k)F
(l,k)c,tx
ji(l,k)c,tyzxz
yxz
ji(l,k)zP
klFWxP
tcklyyxx
tclsl
dl
yy
tclsl
dl
xx
ij
ctlk
kl
tckl
tcji
ij
clktcji
ij
ctlk
tckltcji
ij
ctlk
tc
ij
ctlklk
tc
kltckllk
tclktclktclktckl
Ak Ak
c
c
tckltclk
Ak Ak
c
c
tckltclk
l l
l l
WDM Network Design 80
Shared Path Protection case VWP, RF
(l,k)F
n)cr
lllkl
RFW
Rrr
cvr
kl
nc
klnc
kl
nc
ncnc
n
cnc
kll
integer
,( integer 'Integrity
)( '),,(
''
Capacity
'itySolenoidal
,
,
),(),(
,
),(
,,
,
),('
New symbols
– Rl,k includes all the working-spare routes whose working path is routed on link l,k
– Rl’(l,k)
includes all the working-spare routes whose working path is routed on
bidirectional link l′ and whose spare path is routed on link (l, k)
Similar formulations can be found in [MiSa99], [RaMu99] , [BaBaGiKo99],
WDM Network Design 81
Shared Path Protection case WP, RF
All the previous formulations and a additional one can be found in [CoToMaPaMa03].
(l,k)F
)ncr
lllkl
RFW
Rrr
cvr
kl
nc
klnc
kl
nc
ncnc
n
cnc
kll
integer
,,,( integer 'Integrity
)( ,'),,(
''
Capacity
'itySolenoidal
,
21,,
1
),,(),,(
,
),(
,,,,
,,
2,1
22)2,,(
'
2,12,1
2,1
New symbols
– Variable rc,n,λ1,λ2, where λ1 indicates the wavelength of the working path and λ2
indicates the wavelength of the spare path.
– includes all the working-spare routes, whose working path is routed on
bidirectional link l’ and whose spare path is routed on link (l, k).
)2,,(
'
kl
lR
WDM Network Design 82
Link Protection
Dedicated Link Protection (DLP)
– Each link is protected by providing an alternative routing for all the WDM channels in all the fibers
– Protection switching can be performed by fiber switches (fiber cross-connects) or wavelength switches
– Signaling is local; transit OXCs of the protection route can be pre-configured
– Fast reaction to faults
– Some network fibers are reserved for protection
Shared Link Protection (SLP)
– Protection fibers may be used for protection of more than one link (assuming single-point of failure)
– The capacity reserved for protection is greatly reduced
C o n n e c t i o n
N o r m a l O M S p r o t e c t i o n
( l i n k p r o t e c t i o n )
WDM Network Design 83
Different protected objects
are switched
1) Fiber level
2) Wavelength level
Link Protection
FAULT EVENT (1)
(2)
WDM Network Design 84
Link Protection VWP, FF (Fiber Protection Switch)
(l,k)F
c,(l,k)
qL(l,k)
x
Y
klFWx
qLlqlF
LlF
YY
clsiv
div
xx
kl
ckl
qLkl
c
klckl
qLklAk qLklAk
qL
qL
qLlkqLkl
Ak Ak
cc
cc
clkckl
l l
l l
integer
),(,
integer Integrity
),(Capacity
),(,
otherwise0
if
if
(spare)
itySolenoidal
,
otherwise0
if
if
(working)
itySolenoidal
,
,,
),(,,
,,,
),,( ),,(
.
,
),(,),(,,
,,,,
New symbols
– Y(l,k),(L,q) expresses the number of backup fibers needed on link (l,k) to protect link
(L,q) failure
WDM Network Design 85
Link Protection Cost functions and sharing constraints
Cost function (dedicated case)
Cost function (shared case)
OSS. Wavelength channel level protection design
– Relaxing the integer constraints on Y, each channel is independently protected
protected (while not collecting all the channels owing to the same fiber)
See also [RaMu99]
kl qL qLklkl kl YF
, , ),(,,, , min
),(),, s.t.
min
),(,,,
, ,, ,
qLk(lYT
TF
qLklkl
kl klkl kl
WDM Network Design 86
Link Protection Summary results
Comparison between different protection technique on fiber needed to support the same amount of traffic
Switching protection objects at fiber or wavelength level does ot sensibly affects the amount of fibers.
– This difference increase with the number of wavelength per fiber
WDM Network Design 87
e.g., STM1
@ 155,52 Mbps
e.g., OTN G.709
@ 2.5, 10, 40 Gbps
A Big Difference between Electronic Traffic Requests
and Optical Lightpath Capacity !
Optical transmission
WDM Layer
SDH ATM IP ...
... Electronic
layers
Optical
layers
Electronic
connection
request
Lightpath
connection
provisioning
Traffic Grooming Definition
Optical WDM network – multiprotocol transport platform
– provides connectivity in the form of optical circuits (lightpaths)
WDM Network Design 88
WDM Network Design 89
Traffic Grooming Multi-layer routing
1
2 3
4
5 6
7
Lp1
Lp2
Lp3
Lp4
Physical Topology
Logical Topology
ADMADM
ADMADM
ADMADM
ADMADM ADMADM
ADMADM
ADMADM
1
2 3
4
5 6
7
Suppose Lightpath Capacity: 10
Gbit/sec
EXAMPLE CONNECTIONS
ROUTING
C1 (STM1 between 4 →2) on Lp1
C2 (STM1 between 4 →7) on Lp1
and Lp2
C3 (STM1 between 1 →5) on Lp3
C4 (STM1 between 4 →6) on Lp1
and Lp2 and Lp4
WDM Network Design 90
WDM Network Design 91
Formulation (Keyao Zhu JSAC03)
WDM Network Design 92
Logical Operators: AND, OR, XOR, XNOR
AND, OR, XOR etc can be expressed by using binary variables
1
0
1
0
1
0
1 0
1 0 1 0 AND OR XOR
0 0
1 0
1 1
1 0
0 1
1 0
yxz
yz
xz
1
yxz
yz
xz
1
0
1 0 XNOR
1 0
0 1
Robert G. Jeroslow, “Logic-based decision support: mixed integer model formulation”,
North-Holland, 1989 ISBN 0444871195
rtz
yxt
yxr
OR
AND
)y (1 XORxz
WDM Network Design 93
Some other linear operations
WDM Network Design 94
Logical Operators: AND, OR, XOR, XNOR
AND, OR, XOR etc can be expressed by using binary variables
Negated operators (NAND, NOR, XNOR) are implemented with an
additional variable z = 1 - y, where y is the “direct” operation
1
0
1
0
1
0
1 0
1 0 1 0 AND OR XOR
0 0
1 0
1 1
1 0
0 1
1 0
21
21,
xxy
xxy
1
,
21
21
xxy
xxy
21
12
21
21
2 xxy
xxy
xxy
xxy
WDM Network Design 95
Logical Operators: AND, OR, XOR, XNOR
Also, they can be extended to a general N-variable case:
N
i
i
N
i
i
xy
xyM
1
1
N
i
i
i
Nxy
Nixy
1
)1(
],1[
AND OR
N
i
i
i
xy
Nixy
1
],1[
XOR
or
Arbitrarily large number (at
least equal to N)
Probably no simpler option
exists
...)) (
(
XORXOR
XORXOR
3
21
x
xxy
WDM Network Design 96
References
Articles – [WaDe96] N. Wauters and P. M. Deemester, Design of the optical path layer in multiwavelength cross-
connected networks, Journal on selected areas on communications,1996, Vol. 14, pages 881-891, June
– [CaPaTuDe98] B. V. Caenegem, W. V. Parys, F. D. Turck, and P. M. Deemester, Dimensioning of
survivable WDM networks, IEEE Journal on Selected Areas in Communications, pp. 1146–1157, sept 1998.
– [ToMaPa02] M. Tornatore, G. Maier, and A. Pattavina, WDM Network Optimization by ILP Based on Source
Formulation, Proceedings, IEEE INFOCOM ’02, June 2002.
– [CoMaPaTo03] A.Concaro, G. Maier, M.Martinelli, A. Pattavina, and M.Tornatore, “QoS Provision in Optical
Networks by Shared Protection: An Exact Approach,” in Quality of service in multiservice IP Networks, ser.
Lectures Notes on Computer Sciences, 2601, 2003, pp. 419–432.
– [ZhOuMu03] H. Zang, C. Ou, and B. Mukherjee, “Path-protection routing and wavelength assignment (RWA)
in WDM mesh networks under duct-layer constraints,” IEEE/ACM Transactions on Networking, vol. 11, no.
2, pp.248–258, april 2003.
– [BaBaGiKo99] S. Baroni, P. Bayvel, R. J. Gibbens, and S. K. Korotky, “Analysis and design of resilient
multifiber wavelength-routed optical transport networks,” Journal of Lightwave Technology, vol. 17, pp. 743–
758, may 1999.
– [ChGaKa92] I. Chamtlac, A. Ganz, and G. Karmi, “Lightpath communications: an approach to high-
bandwidth optical WAN’s,” IEEE/ACM Transactionson Networking, vol. 40, no. 7, pp. 1172–1182, july 1992.
– [RaMu99] S. Ramamurthy and B. Mukherjee, “Survivable WDM mesh networks, part i - protection,”
Proceedings, IEEE INFOCOM ’99, vol. 2, pp. 744–751, March 1999.
– [MiSa99] Y. Miyao and H. Saito, “Optimal design and evaluation of survivable WDM transport networks,”
IEEE Journal on Selected Areas in Communications, vol. 16, pp. 1190–1198, sept 1999.
WDM Network Design 97
References
– [BaMu00] D. Banerjee and B. Mukherjee, “Wavelength-routed optical networks: linear formulation, resource
budgeting tradeoffs and a reconfiguration study,” IEEE/ACM Transactions on Networking, pp. 598–607, oct
2000.
– [BiGu95] D. Bienstock and O. Gunluk, “Computational experience with a difficult mixed integer
multicommodity flow problem,” Mathematical Programming, vol. 68, pp. 213–237, 1995.
– [RaSi96] R. Ramaswami and K. N. Sivarajan, Design of logical topologies for wavelength-routed optical
networks, IEEE Journal on Selected Areas in Communications, vol. 14, pp. 840{851, June 1996.
– [BaMu96] D. Banerjee and B. Mukherjee, A practical approach for routing and wavelength assignment in
large wavelength-routed optical networks, IEEE Journal on Selected Areas in Communications, pp. 903-
908,June 1996.
– [OzBe03] A. E. Ozdaglar and D. P. Bertsekas, Routing and wavelength assignment in optical networks,
IEEE/ACM Transactions on Networking, vol. 11, no. 2, pp. 259-272, Apr 2003.
– [KrSi01] Rajesh M. Krishnaswamy and Kumar N. Sivarajan, Design of logical topologies: A linear formulation
for wavelength-routed optical networks with no wavelength changers, IEEE/ACM Transactions on
Networking, vol. 9, no. 2, pp. 186-198, Apr 2001.
– [FuCeTaMaJa99] A. Fumagalli, I. Cerutti, M. Tacca, F. Masetti, R. Jagannathan, and S. Alagar, Survivable
networks based on optimal routing and WDM self-heling rings, Proceedings, IEEE INFOCOM '99, vol. 2, pp.
726-733,1999.
– [ToMaPa04] M. Tornatore and G. Maier and A. Pattavina, Variable Aggregation in the ILP Design of WDM
Networks with dedicated Protection , TANGO project, Workshop di metà progetto , Jan, 2004, Madonna di
Campiglio, Italy
WDM Network Design 98
Outline
Introduction to WDM network design and optimization
Integer Linear Programming approach to the problem
Physical Topology Design
– Unprotected case
– Dedicated path protection case
– Shared path protection case
– Link protection
Heuristic approach
WDM Network Design 99
Heuristic: method based on reasonable choices in RFWA that lead
to a sub-optimal solution
– Connections are routed one-by-one
– In this case we will refer to an example, based on the concept of
auxiliary graph
Heuristic strategies can be:
– Deterministic: greedy vs. local search
• Generic definitions in the following, together with a large example
– Stochastic:
• E.g.:simulated annealing, tabu search, genetic algorithms
• Not covered in this course
WDM mesh network design Heuristic approaches
WDM Network Design 100
Greedy Heuristic (1) Framework
Greedy
– Builds the solution step by step starting from scratch
– Starts from an empty initial solution
– At each iteration an element is added to the solution, such that
• the partial solution is a partial feasible solution, namely it is possible to build
a feasible solution starting from the partial one
• the element added to the solution is the best choice, with respect to the
current partial solution (the greedy is a myopic algorithm)
Features
– Once a decision is taken it is not discussed anymore
– The number of iterations is known in advance (polynomial)
– Optimality is usually not guaranteed.
WDM Network Design 101
Greedy Heuristic (2)
We have to define
– Structure of the solutions and the elements which belong to it
– Criterion according to which the best element to be added is chosen
– Partial solution feasibility check
WDM Network Design 102
Greedy Heuristic (3) Algorithm scheme
WDM Network Design 103
Local search Heuristic (1) Framework
Given a feasible solution the Local Search tries to improve it.
– Starts with an initial feasible solution: the current solution x∗
– Returns the best solution found xb
– At each iteration a set of feasible solutions close to the current one, the
neighborhood N(x∗), is generated
– A solution x is selected among the neighbor solutions, according to a
predefined policy, such that x improves upon x∗
– If no neighbor solution improves upon the current one, (or stopping
conditions are verified,) the procedure stops, otherwise xb = x∗= x
WDM Network Design 104
Local search Heuristic (2) Remarks
– Local search builds a set of solutions
– The set of neighbor solutions is built by partially modifying the current
solution applying an operator called move
– Each neighbor solution can be reached from the current one by applying
the move
– Local search moves from feasible solution to feasible solution
– Local search stops in a local optimum
We have to define
– The initial solution
– The way on which the neighborhood is generated:
• The solution representation: a solution is represented by a vector x
• The move which is applied to build the neighbors
• selection policy
• (stopping conditions)
WDM Network Design 105
Local search Heuristic (3) Algorithm scheme
WDM Network Design 106
Static WDM mesh networks Optimization problem definition
Design problem
Routing, fiber and wavelength assignment for each lightpath
Design variables
Number of fibers per link
Flow/routing variables
Wavelength variables
Cost function: total number of fibers
Scenarios:
With or without wavelength conversion
WDM Network Design 107
Heuristic for static design (RFWA) A deterministic approach for fiber minimization
Optimal design of WDM networks under static traffic
A deterministic heuristic method based on one-by-one RFWA
is applied to multifiber mesh networks:
– RFWA for all the lightpaths is performed separately and in
sequence (greedy phase)
– Improvement by lightpath rerouting (consolidation phase)
It allows to setup lightpaths so to minimize the amount of fiber
deployed in the network
WDM Network Design 108
Heuristic static design (RFWA) Network and traffic model specification
Pre-assigned physical topology graph (OXCs and WDM links)
– WDM multifiber links
• Composed of multiple unidirectional fibers
• Pre-assigned number of WDM channels per fiber (global network variable W)
– OXCs
• Strictly non-blocking space-switching architectures
– In short, no block in the nodes
• Wavelength conversion capacity: 2 scenarios
– No conversion: Wavelength Path (WP)
– Full-capability conversion in all the OXCs: Virtual Wavelength Path (VWP)
Pre-assigned logical topology
– Set of requests for optical connections
• OXCs are the sources and destinations (add-drop function)
• Multiple connections can be demanded between an OXC pair
• Each connection requires a unidirectional lightpath to be setup
WDM Network Design 109
Heuristic static design (RFWA) Routing Fiber Wavelength Assignment (RFWA)
(Some possible) Routing criteria
– Shortest Path (SP) selects the shortest source-
destination path (# of crossed links)
• Different metrics are possible, e.g.:
– Number of hops (mH)
– Physical link length in km (mL)
– Least loaded routing (LLR) avoids the busiest links • E.g., among the k-shortest paths, choose the one whose most loaded link is less loaded
– Least loaded node (LLN) avoids the busiest nodes
WDM Network Design 110
Heuristic static design (RFWA) Routing Fiber Wavelength Assignment (RFWA)
Wavelength assignment algorithms
– Pack the most used wavelength is chosen first
– Spread the least used wavelength is chosen first
– Random random choice
– First Fit pick the first free wavelength
Similarly, for fiber assignment criteria
– First fit, random, most used, least used
WDM Network Design 111
Heuristic static design (RFWA) Wavelength layered graph
Physical topology
(3 wavelengths)
2 plane
C. Chen and S. Banerjee: 1995 and 1996
I.Chlamtac, A Farago and T. Zhang: 1996
Equivalent wavelength
layer graph
1 plane
3 plane
OXC with converters
OXC without converters
WDM Network Design 112
Heuristic static design (RFWA) Multifiber (or Extended) wavelength layered graph
Physical topology (2 fiber links, 2 wavelengths)
Different OXC functions displayed on the layered graph
– 1 - add/drop
– 2 - fiber switching
– 3 - wavelength conversion
– 3 - fiber switching + wavelength conversion
WDM Network Design 113
Heuristic static design (RFWA) Multifiber (extended) wavelength layer graph
Enables the joint solution of R,F
and W in RFWA
Network topology is replicated
W·F times and nodes are
opportunely linked among various
layers
WDM Network Design 114
Heuristic static design (RFWA) Layered graph utilization
The layered graph is “monochromatic”
Routing, fiber and wavelength assignment are solved together
Links and nodes are weighted according to the routing, fiber and
wavelength assignment algorithms
The Dijkstra Algorithm is finally applied to the layered weighted
graph
Worst case complexity
N = # of nodes
F = # of fibers
W = # of wavelengths 2
O NFW
WDM Network Design 115
Heuristic: Consolidation Phase Heuristic design and optimization scheme
– Connection request sorting
rules
• Longest first
• Most requested couples
first
• Balanced
• Random
– Processing of an individual
lightpath
• Routing, Fiber and
Wavelength Assignment
(RFWA) criteria
• Dijkstra’s algorithm
performed on the
multifiber layered graph
Sort connection
requests
Idle network,
unlimited fiber
Setup the lightpaths
sequentially
Prune unused fibers
Identify fibers with
only k used s
Prune unused fibers
Attempt an alternative
RFWA for the identified lightpaths
for
k = 1 to W
WDM Network Design 116
Heuristic for WDM mesh networks design Case-study
National Science
Foundation Network
(NSFNET): USA
backbone
Physical Topology
– 14 nodes
– 44 unidirectional links
Design options
– W: 2, 4, 8, 16, 32
– 8 RFWA criteria
WDM Network Design 117
Heuristic static design (RFWA) RFWA-criteria labels
WDM Network Design 118
Heuristic static design (RFWA) Total number of fibers
Hop-metric minimization performs
better
– Variations of M due to RFWAs and
conversion in the mH case below
5%
0
100
200
300
400
500
0
100
200
300
400
500
2 4 8 16 32
404
207
109
59.7
36.2
410
213
114
64.5
39.4
VWP WP
To
tal fib
er
num
ber,
M
Number of wavelengths, W
.
0
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
0
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
C 3 C 1 C 7 C 5 C 4 C 2 C 8 C 6
2 4 8 1 6 3 2
S P L L R S P L L R S P L L R S P L L R
V W P W P V W P W P
m H m L
The initial sorting rule
resulted almost irrelevant for
the final optimized result
(differences between the
sorting rules below 3%)
To
tal fib
er
num
ber,
M
WDM Network Design 119
Heuristic static design (RFWA) Fiber distribution in the network
– NSFNet with W = 16 wavelengths per fiber, mL SP RFWA criteria
– The two numbers indicate the number of fibers in the VWP and WP
network scenarios
– Some links are idle
(3,4)
(5,6)
(2,2)
(6,6)
(2,2)
(2,2)
(6,5) (6,6)
(6,5)
(2,2)
(0,1)
(2,2)
(2,2)
(2,2) (2,3)
(2,2)
(2,2)
(0,0) (4,4)
(4,4)
(4,4)
(0,0)
WDM Network Design 120
Heuristic static design (RFWA) Wavelength conversion gain
Wavelength converters are more effective in reducing the
optimized network cost when W is high
0
2
4
6
8
10
0
2
4
6
8
10
2 4 8 16 32
1.6
3
3.0
8
4.5
6
7.3
6
8.2
4
M g
ain
fa
cto
r, G M
Number of wavelengths, W
GM MWP MVWP
MWP
100
WDM Network Design 121
Heuristic static design (RFWA) Saturation factor
0
0.2
0.4
0.6
0.8
1
1.2
0
0.2
0.4
0.6
0.8
1
1.2
2 4 8 16 32
VWP WP
0.9
85
0.9
7
0.9
29
0.8
62
0.7
58
0.9
72
0.9
36
0.8
84
0.7
87
0.6
68
Number of wavelengths, W
Sa
tura
tion
fa
cto
r, r
. .
L L R L L R L L R L L R
V W P W P
m L m H m L m H
S P S P S P S P
0 . 6
0 . 6 5
0 . 7
0 . 7 5
0 . 8
0 . 8 5
0 . 9
0 . 9 5
1
0 . 6
0 . 6 5
0 . 7
0 . 7 5
0 . 8
0 . 8 5
0 . 9
0 . 9 5
1
C 1 C 3 C 2 C 4 C 6 C 8 C 5 C 7
2 4 8 1 6 3 2
r
A coarser fiber granularity allows us to save
fibers but implies a smaller saturation factor
VWP performs better than WP
– Variations of r due to RFWAs and metrics in
the VWP case below 5%
r C
W M
C = number of used
wavelength channels
Sa
tura
tion
fa
cto
r,
WDM Network Design 122
Heuristic static design (RFWA) Optimization: longer lightpaths...
Compared to the initial
routing (shortest path,
which is also the
capacity bound) the fiber
optimization algorithm
increases the total
wavelength-channel
occupation (total
lightpath length in
number of hops)
– C is increased of max
10% of CSP in the worst
case
C CSP
CSP
100
CSP = number of used wavelength channels with SP
routing and unconstrained resources (capacity bound)
0
2
4
6
8
10
12
2 4 8 16 32
2.1
8
2.3
7
3.8
6 4.6
2
9.6
1
2.2
3
1.9
3
3.3
9
3.6
6
VWPWP
Ca
pa
city b
ou
nd
pe
r ce
nt d
evia
tio
n
Number of wavelengths, W
mH cases
,
WDM Network Design 123
Heuristic static design (RFWA) …traded for fewer unused capacity
U 1 C
W M
100
Compared to the initial
routing (shortest path) the
fiber optimization algorithm
decreases the total number
of unused wavelength-
channels
– U is halved in the best
case Notes
– Initial SP routing curve:
data obtained in the VWP
scenario (best case)
– Optimized solution curve:
averaged data
comprising the WP and
VWP scenarios
0
10
20
30
40
50
0 5 10 15 20 25 30 35
initial SP routingoptimized solution
% U
nu
se
d c
ap
acity, U
Number of wavelengths, N
WDM Network Design 124
Heuristic static design (RFWA) Convergence of the heuristic optimization
The algorithm appears to converge well before the last iteration
Improvements of the computation time are possible
Notes:
– Convergence is rather insensitive to the initial sorting rule and to the RFWA criteria
55
60
65
70
75
80
85
90
6 104
6.5 104
7 104
7.5 104
8 104
8.5 104
9 104
9.5 104
0 2 4 6 8 10 12 14 16
VWPW=16, mH, SP
M L
To
tal fib
er
nu
mb
er,
M
To
tal fib
er le
ng
th, L
(km
)
optimization counter, k
WDM Network Design 125
Case-study networks Comparison of SF with heuristic optimization (VWP)
ILP by SF is a useful benchmark to verify heuristic dimensioning
results
– Approximate methods do not share this property
.
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
3 0 0
3 5 0
4 0 0
0 5 1 0 1 5 2 0 2 5 3 0 3 5
N S F N E T V W P
s o u r c e f o r m . h e u r i s t i c
Number of wavelengths, W
To
tal fibe
r n
um
ber,
M
0
2 0 0
4 0 0
6 0 0
8 0 0
1 0 0 0
1 2 0 0
1 4 0 0
1 6 0 0
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
E O N V W P
s o u r c e f o r m .
h e u r i s t i c
Number of wavelengths, W
To
tal fib
er
nu
mb
er,
M
WDM Network Design 126
Heuristic static design (RFWA) Concluding remarks
A heuristic method for multifiber WDM network optimization
under static traffic has been proposed and applied to various
physical network scenarios
Good sub-optimal solutions in terms of total nr of fibers can be
achieved with a reasonable computation time
The method allows to inspect various aspects such as RFWA
performance comparison and wavelength conversion
effectiveness
Future possible developments
– Upgrade to include also lightpath protection in the WDM layer
– Improvement of the computation time / memory occupancy
WDM Network Design 127 127
Politecnico
di Milano
Past / current research lines Industrial partnerships
OTN
design and simulation
Semi-transparent
OTN, physical
impairments;
ASON/GMPLS control
plane
1996
year
2000 2003 2006 2007 2008
Resilience,
protection, availability
Multi-domain
routing
Multi-layer TE,
learning
algorithms
SLA-aware routing;
Submarine
WDM Network Design 128 128
Politecnico
di Milano
Past / current research lines Network design and simulation tools
OTN
design and simulation
Semi-transparent
OTN, physical
impairments;
ASON/GMPLS control
plane
1996
year
2000 2003 2006 2007 2008
Resilience,
protection, availability
Multi-domain
routing
Multi-layer TE,
learning
algorithms
SLA-aware routing;
Carrier-grade
Ethernet
OPTCORE AGNES
WDM Network Design 129 129
OptCore: the WDM optimization tool
Finds the best matching between the physical topology and the set of requests for lambda connections
Supports all the main WDM-layer protection techniques
Provides data for OXC and OADM configuration
Allows to inspect and try several network scenarios, including transparent, opaque or partially-opaque WDM networks
Solves green-field design as well as network re-design under legacy element constraints
Is applicable to large systems with 128 and more wavelengths per fiber, multi-fiber links and high-dense connectivity
Performs dynamic-traffic simulation to assess the capability of a network to support unexpected lambda connection requests and traffic expansion
OptCore is the tool to assist WDM network operators in
their offline design and optimization duty
WDM Network Design 130 130
OptCore architecture and scheme
Network physical
topology (links and nodes)
Wavelength-conversion
capability
Number of wavelengths
per fiber (W)
Protection scheme (e.g.
unprotected, dedicated, shared)
Routing, fiber and wavelength
assignment algorithms P
ro
cessin
g to
ol
Working and spare
resources allocation
OXC and converters
configuration
Cost-function
minimization U
se
r in
te
rfa
ce
(X
ML
-b
ase
d)
OC-layer topology
(OC request matrix)
Initial conditions
(e.g. initial # fibers) U
se
r in
te
rfa
ce
(X
ML
-b
ase
d)
WDM Network Design 131 131
OptCore graphical interface Workspace window
WDM Network Design 132 132
OptCore graphical interface Output display (I)
WDM Network Design 133 133
OptCore graphical interface Output display (II)
WDM Network Design 134 134
Integer Linear Programming (ILP)
– The most general exact method
– Exponential computational complexity not scalable
– The number of variables and constraints is huge
• It can be often decreased by choosing an appropriate
formulation (e.g. constrained-route, source, etc.)
– Variables defined in the integer domain
• Branch and bound technique required
Heuristic methods
– Polynomial-complexity algorithms
– No guarantee that the solution found is the optimum
• Close to ILP results in many tested cases
– A very good alternative to ILP for realistic-dimension
problems
OptCore: optimization problem solution Optimization methods
Sim
pli
cit
y
Pre
cis
ion
ILP
Heuristics
WDM Network Design 135
Additional slides on Bhandary’s algorithm for link-disjoint paths
Courtesy of Grotto Networking
WDM Network Design 136
Diverse Route Computation
Problem:
– Find two disjoint paths between the same source
and destination, with minimum total cost (working
+ protection)
• We may want the paths node diverse (stronger)
Applications:
– Dedicated Path Protection
WDM Network Design 137
2-step: diverse paths via pruning
NE
1
NE
3
NE
5
NE
2
NE
4
NE
6
8
4
2
1 1 1
NE
7
2
2
8
NE
8
2
2
Find the first shortest path, then prune those links
Primary path
cost = 3
WDM Network Design 138
2-step: diverse paths via pruning
Find the second shortest path in the modified graph
NE
1
NE
3
NE
5
NE
2
NE
4
NE
6
8
4
2
NE
7
2
2
8
NE
8
2
2
Backup path
cost = 12
Total for both
paths= 15
WDM Network Design 139
2-step: diverse paths via pruning
Questions
– Are these the lowest cost set of diverse paths?
• Why should they be? We computed each separately…
– Are there situation where this approach will completely fail?
• Let’s look at another network…
WDM Network Design 140
2-step approach on trap topology
Step 1. Find the
shortest path from
source to destination
Step 2. Prune out links
from the path of step 1.
NE
1
NE
3
NE
5
NE
2
NE
4
NE
6
2
2 2
2
1 1 1
WDM Network Design 141
2-step approach on trap topology
Step 3. Can’t find another
path from 1 to 6 since we
just separated the graph
Hmm, maybe a solution
doesn’t exist? Or maybe
we need a new algorithm?
NE
1
NE
3
NE
5
NE
2
NE
4
NE
6
2
2 2
2
WDM Network Design 142
Diverse Path Calculation Methods
Algorithms: – Bhandari’s method utilizing a modified Dijkstra algorithm
twice. [Ramesh Bandari, Survivable Networks, Kluwer, 1999]
– Suurballe’s algorithm: transforms the graph in a way that two regular Dijkstra computations can be performed.
NE
1
NE
3
NE
5
NE
2
NE
4
NE
6
2
2 2
2
1 1 1
Answer: Find a better
algorithm
WDM Network Design 143
Diverse Path Algorithm: Example
1
1 1
4
3
A Z
C
B
Step1: Compute least cost primary path
Primary path is A-B-C-Z, cost=3
WDM Network Design 144
Diverse Path Algorithm: Example
Step2: Treat graph as directed. In all edges in the primary path: Set forward
cost to . Set reverse cost to negative of original cost.
-1
-1 -1
4
3
A Z
C
B
3 4
WDM Network Design 145
Diverse Path Algorithm: Example
Step3: Find least cost back-up path
-1
-1 -1
4
3
A Z
C
B
3 4
Back-up path is A-C-B-Z, cost=6
WDM Network Design 146
Diverse Path Algorithm: Example
Step4: Merge paths. Remove edges where primary and back-up traverse
in opposite directions
4 -1
-1 -1 3
A Z
C
B
3 4
New primary is A-B-Z, back-up is A-C-Z, total cost = 9
WDM Network Design 147
BACKUP SLIDES
WDM Network Design 148
Outline
Introduction to WDM network design and optimization
Integer Linear Programming approach
Physical Topology Design
– Unprotected case
– Dedicated path protection case
– Shared path & link protection cases
– p-Cycles
Heuristic approach
WDM Network Design 149
Link Protection: p-Cycles (I)
A p-cycle (“preconfigured protection cycle”) is the most efficient
structure for preconfigured restoration in terms of capacity efficiency
p-cycles go beyond the behavior of a ring
– Emulate the ring behavior for a class of failures (faults of the peripheral
segments of the cycle)
– Protect all its chord links like a mesh network, by providing two
restoration paths
– Recovery action is the same as in bidirectional-line switching rings (e.g.,
SONET/SDH 2-fiber SPRings)
– No signaling is needed to activate restoration
Optimal p-cycle selecting (NP-hard problem): a trade off between
minimizing path length and spare capacity
WDM Network Design 150
Link Protection: p-Cycles (II)
The failure of a peripheral link of
the p-cycle is bypassed using the
only restoration path available
Like a self-healing ring
peripheral link
chord link
P-cycle
WDM Network Design 151
Link Protection: p-Cycles (III)
For the failure of a chord link of
the p-cycle two restoration paths
are available
K > 100%
– In the example
%33%100299
9
K
WDM Network Design 152
An ILP Model for p-Cycles VWP, FF
(l,k)F
c,(l,k)
qL(l,k)
x
Y
klFWax
klna
klnyx
clsiv
div
xx
kl
ckl
qLkl
c
klklckl
p
ppklkl
p
ppkl
c
ckl
Ak Ak
cc
cc
clkckl
l l
integer
),(,
integer Integrity
),(Capacity
),(
),(
cycles-p
,
otherwise0
if
if
(working)
itySolenoidal
,
,,
),(,,
,,,,
,,,
,,,,
,,,,
New symbols
P : Set of p-cycles indexed by p
πp,l,k : equal to 1 if p-cycle p crosses link (l,k), otherwise it will be equal to 0
yplk : equal to 1 if the p-cycle p protects link (l,k) as on cycle span, equal to 2 if p-
cycle p protects span (l,k) as straddling span and 0 otherwise.
WDM Network Design 153
How do you calculate good candidates for p-cycles?
WDM Network Design 154
Path-protected WDM mesh networks
Optimal design of WDM networks under static traffic with
dedicated path-protection (1+1 or 1:1)
– It allows to setup protected lightpaths so to minimize the amount of
fibers deployed in the network (RFWA)
– Each connection request is satisfied by setting up a working-
protection (W-P) lightpath pair under the link-disjoint constraint
WDM Network Design 155
Lightpaths and Wavelength Routing
Lightpath
Virtual topology
Wavelength-continuity
constraint
Wavelength conversion